Weber's theorem (Algebraic curves)

In mathematics, Weber's theorem, named after Heinrich Martin Weber, is a result on algebraic curves. It states the following.

Consider two non-singular curves C and C′ having the same genus g > 1. If there is a rational correspondence φ between C and C′, then φ is a birational transformation.

References

• Coolidge, J. L. (1959). A Treatise on Algebraic Plane Curves. New York: Dover. p. 135. ISBN 0-486-60543-4.
• Weber, H. (1873). "Zur Theorie der Transformation algebraischer Functionen" (PDF). Journal für die reine und angewandte Mathematik (in German). 76: 345–348. doi:10.1515/crll.1873.76.345.

Further reading

• Tsuji, Masatsugu (1941). "Theory of conformal mapping of a multiply connected domain". Japanese Journal of Mathematics :Transactions and Abstracts. 18: 759–775. doi:10.4099/jjm1924.18.0_759.

External links

• Weisstein, Eric W. "Weber's Theorem". MathWorld.